A major problem of xenotransplantation in recipient animals (e.g., humans) that do not express the enzyme UDP-galactose: β-D-galactosyl-1,4-N-acetyl-D-glucosaminide α-1,3 galactosyl-transferase (α-1,3 galactosyltransferase; “αGT”) that catalyzes the formation of the terminal disaccharide structure, galactose α-1,3 galactose (“αgal”), is the hyperacute rejection of xenografts in such recipients that is largely, if not exclusively, due to the action of antibodies specific for the αgal epitope on the surface of cells in the xenograft. Transgenic animals (e.g., pigs) have been derived which lack, or substantially lack, functional αGT and thus also lack, or substantially lack, αgal epitopes.